Abstract

Quantum correlation and its measurement are essential in exploring fundamental quantum physics problems and developing quantum-enhanced technologies. A quantum correlation may be generated and manipulated in different spaces, which demands different measurement approaches corresponding to the position, time, frequency, and polarization of quantum particles. In addition, after early proof-of-principle demonstrations, it is of great demand to measure quantum correlation in a Hilbert space large enough for real quantum applications. When the number of modes goes up to several hundreds, the single-mode addressing becomes economically unfeasible, and the processing of correlation events with hardware also becomes extremely challenging. Here, we present a general and large-scale measurement approach of the Correlation on the Spatially Mapped Photon-Level Image. The quantum correlations in other spaces are mapped into the position space and are captured by a single-photon-sensitive imaging system. Synthetic methods are developed to suppress noises so that single-photon registrations can be faithfully identified in images. We eventually succeeded in retrieving all the correlations with a big-data technique from tens of millions of images.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. INTRODUCTION

Quantum correlation, as one of the unique features of quantum theory, plays a crucial role in quantum information applications. After experiencing quantum evolution, for instance, quantum interference, quantum particles can be correlated in more diverse ways than the classical counterpart. For example, Hong–Ou–Mandel (HOM) interference can reveal the nonclassical bunching properties of photons [1]. These correlation characteristics are crucial in quantum computing [2,35], quantum simulation [69], and quantum communication [1013].

In theory, especially in the field of quantum computing, if we managed to send enough entangled photons into plenty of modes and operate their superposition states simultaneously, we would be able to obtain a sufficiently large quantum state space that may enable a higher computational power than classical computers. In practice, it may still be acceptable to place a single-photon detector behind each spatial mode for comparably small systems [9,1416]. However, it will become both technically challenging and economically unfeasible to address thousands of modes simultaneously with single-photon detectors, thus creating a decisive bottleneck that would prevent from detecting state spaces large enough for real quantum applications.

Thankfully, recent advances in charge-coupled device (CCD) cameras make it possible to directly image spatial output results at a single-photon level [1724]. HOM interference was also successfully verified by the low-noise correlation detection on two modes with an intensified camera [25].

An alternative and elegant approach presented in this work is to convert the modes from different degrees of freedom into the modes in position, and then measure all the spatial modes accordingly by the large number of units in single-photon-sensitive cameras. We call this general and large-scale measurement approach the Correlation on the Spatially Mapped Photon-Level Image (COSPLI). We have also developed the methods to retrieve the low-noise signal of single-photon registrations and their correlations from tens of millions of images. As an example for applications, we experimentally demonstrate our COSPLI by measuring the spectral correlations [26,2729] of parametric down-conversion photons.

2. EXPERIMENT

COSPLI can generally be achieved in five steps [Fig. 1(a)]. The first step is to identify the target space where the correlation exists. The quantum states of a single photon can be expressed in various eigenvectors with corresponding eigenvalues, such as the position, time, frequency, and polarization. The target space can be whichever space needed to measure. In Fig. 1(a), we use symbols {u1i} and {u2j} to represent the target variables. In our experiments, we detect a joint spectrum of correlated photons to demonstrate this technique. Under this circumstance, the target is the spectrum or the frequency space.

 figure: Fig. 1.

Fig. 1. (a) Schematic of COSPLI. (b)–(d) Sketched solutions of mapping different variables into positions. (b) Mapping frequency to position. (c) Mapping time to position. TDFS represents a time-dependent frequency shifter. (d) Mapping polarization to position. (e) Experimental setup of mapping frequency to position and joint spectrum measurement. A mode-lock Ti:sapphire oscillator centered at 780 nm, with a laser pulse duration of 130 fs and a repetition rate of 77 MHz, pumps a 1.3-mm-thick LiB3O5 (LBO) crystal to double the laser frequency to 390 nm. The ultraviolet laser then pumps a 2-mm-thick β-BaB2O4 (BBO) crystal to create identical photon pairs via a χ(2) Type 2 spontaneous parametric down-conversion process in the beam-like scheme [30]. The correlation of the frequency space of signal and idler photons is mapped into the correlation in the position space by a blazed grating with a line density of 1200 l/mm. (f) The spectra of signal and idler photons derived from the accumulated image. (g) (Top) An accumulated image with all spectral components. The upper and lower spots are signal and idler photons, respectively. (Middle) One of the frames that possess two registered photons. The two shiny spots are distributed in the two characterized areas in the accumulated image, respectively. (Bottom) The white grids define the resolution of the correlation measurement by dividing the mapped space into many individual parts.

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It is usually difficult to detect the target variable directly in a large number of modes. Therefore, a mapping operation is necessary to convert the target to position spaces, {x1i} and {x2j}, which can be measured by a CCD camera. To demonstrate this, we map the frequency information of photons to their positions. In optical system, prisms and gratings are commonly used as spectroscopic devices. To optimize the efficiency and the splitting angle, we chose a blazed grating to transform different frequency components of photons into their corresponding positions. Within a particular wavelength range, the first-order diffracted spot of blazed grating is the brightest, rather than the zero-order reflected spot, which means that the grating loss can be controlled to a relatively low level.

We can divide the target variables into two classes: continuous variables and discrete variables. For continuous variables like the frequency or time, mapping such variables to positions is achievable although it seems difficult. Take time as an example, if the time precision is low, like 103s or longer, mechanical-angle-scanning mirrors can help to reflect photons arriving at different times to different places. However, because mechanical devices cannot reach higher precision, the system will be more complicated in situations where higher precision is required. We propose the use of a time-dependent frequency shifter followed by gratings. By continuously sweeping the frequency shift of an electro-optic modulator or acousto-optic modulator, one can map such continuous variables to different spatial coordinates.

As for discrete variables like polarization, a simple polarization beam splitter will map a pair of orthogonal states to different positions. The most recent record of the maximum number of entangled photons is 12 [31], meaning that the ability to measure the correlation among 24 polarization outputs will be quite sufficient. As the physical systems and the operation complexity increase, this number will be dramatically rising in the future. For a schematic graph, see Figs. 1(b)1(d).

The mapped positions of photons can be either discrete or continuous. For instance, the outputs of a two-dimensional quantum walk from a photonic chip present a discrete spot array. Thus, we are able to directly divide them into several discrete regions according to the location of spots and construct a correlation matrix. As is shown in Fig. 1(a), symbols {x1i} and {x2j} represent different components of converted position variables. In our demonstration experiment, the frequency spectra of photons are continuous, and the converted positions therefore are also continuous. However, in the data analysis process, we have to divide the continuous pattern into equal-size segments. As a result, the continuity of data is destroyed to some extent. Hence, we need to restore its inherent continuity at a later stage.

The forth step is to measure the spatially mapped positions with a proper imaging system. Nowadays, intensified charge-coupled devices (ICCD) and intensified scientific complementary metal oxide semiconductors [32] are being well developed to observe single photons. Their high time resolution can be employed as a temporal filter to suppress noises. We retrieve the spatial information from each frame and retrieve the temporal information from the order of frames. We then can perform the last step, which is to calculate the correlation matrix to analyze the spatial and/or temporal correlation.

Figure 1(g) shows several shiny points that can be distinguished from the background. Although they may be the result of dark counts, these events are all considered to be by actual photons. We assume that the noises are generated with a same probability in every pixel of the camera, resulting in a noise matrix N(ωs,ωi)=pns(ωs)pni(ωi), which means they should just contribute to a contour base of the final correlation matrix as S(ωs,ωi)+N(ωs,ωi). With an optimized criterion, we use a computer program to automatically identify the existence of registered photons and record their positions xs and xi, and then input this correlation information into a correlation matrix S (ωs, ωi) (see Supplement 1).

As an example, we demonstrate a mapping from the frequency correlation to the spatial correlation of photons [see Fig. 1(e)]. Type-II spontaneous parametric down-conversion [33] is applied to generate two frequency-correlated photons, the joint spectrum of which can be written as

Sdep(ωs,ωi)=|f(ωs,ωi)|2=|Aα(ωs+ωi)ϕ(ωs,ωi)|2,
(see Supplement 1). The correlated photons emitted by a beta-barium-borate (BBO) crystal are delivered to the blazed grating. After mapping their frequency information to position information, signal and idler photons are then captured by an ICCD. In the correlation analysis process, we first define the regions where photons will appear by accumulating signal and idler photons on a single image. We then divide the regions of signal and idler photons into 24 and 37 segments, respectively, as shown in Fig. 1(g), with a spatial interval of 10 pixels. Each segment represents one component of the spectrum, and the number of counts of every segment indicates the intensity of each component. In this way, the continuous information in the spectral domain is transformed to the discrete spatial positions. Based on the accumulated intensity and the calibrated spectra, we express the spectrum distribution of the two photons as ps and pi, as shown in Fig. 1(f).

3. RESULTS

COSPLI is a technique that allows the acquisition of spatial-temporal correlation of photons. In our experiments, both time-independent and time-dependent spatial correlations are demonstrated. The time width of the camera gate determines whether photons in one frame share the correlation or not. In the time-independent scenario, we set the ICCD gate width as 10 μs, which is far longer than the pump laser pulse interval (12.9 ns). Hundreds of photon pairs may appear in one frame; however, on account of many factors of loss, only one or two photons finally register in one frame. In this case, photons detected in the same frame are seldom originally generated by the same pump pulse, which means they are not temporally correlated and therefore have no frequency correlation. The statistic characteristic of these photons will be the same as those of an ensemble, where particles are all independent. The correlation matrix turns out to be simply the product of probability distribution:

Sindep(ωs,ωi)=ps(ωs)pi(ωi),
where ps(ωs) and pi(ωi) represent the spectrum distribution of signal and idler photons. Sindep is the joint spectrum intensity matrix, representing the probability that the signal and idler photon simultaneously possess frequencies ωs and ωi, respectively [34]. Unlike the joint spectrum of correlated photons [Eq. (2)], the time-independent one is separable. Figure 2(b) shows the experimental results obtained from 100,000 frames. The perfect similarity with the prediction [Fig. 2(a)] implies that most of shiny points on the screen are real photons rather than dark counts or environmental noise, which can serve as a test of the ICCD single-photon sensitivity.

 figure: Fig. 2.

Fig. 2. Theoretical and experimental results of the correlation measurement. (a) and (b) are theoretical and experimental results of a time-independent joint spectral intensity matrix of photons, respectively. The vertically elliptical shape suggests the photons share no correlation. (c) and (d) are theoretical and experimental results of a time-dependent joint spectral intensity matrix, respectively. The joint spectrum of correlated photons generated by BBO is an obliquely elliptical shape rather than a strict one-to-one relationship, because the two photons are not maximally correlated in the frequency space [34].

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Now we consider the time-dependent scenario, in which only the two correlated photons generated by the same pump pulse appear in the same frame. We synchronize the generation and detection of correlated photons by triggering ICCD with an electric pulse produced by the pump laser oscillator. Another main difference with the time-independent scenario is the gate width. For the purpose of ensuring that every frame contains at most one pair of the correlated photons, the gate width is set as 12.5 ns, which is shorter than the interval between two laser pulses (12.9 ns). In this case, detected photons should share the expected frequency correlation with each other. We put the frames that contain correlation events together in a video (see Visualization 1).

Experimental results from a time-dependent correlation matrix are obtained from 107 frames [see Figs. 2(c) and 2(d)]. The rate of effective correlation events is approximately 103, in which the intrinsically low excitation rate (20%) is an improvable factor. If applying a heralded entanglement source, the rate of effective correlation events will increase substantially [35,36]. There is a tradeoff between the resolution and the count rate, and we choose 10 pixels as the interval between two components, which provide a resolution of 0.74 nm according to the calibrated spectrum distribution.

To demonstrate COSPLI with a different joint spectrum, we use bandpass filters to release the frequency correlation, which is also an important operation to produce high-purity single photons [37]. The transmission spectrum of 3 nm filters centered at 779.5 nm is shown in Fig. 3(a). The two filters lead to a scissor matrix defined as G(ωs,ωi)=gs(ωs)gi(ωi), where gs(ωs) and gi(ωi) are the transmission probabilities of the signal and idler photons, respectively. By multiplying the theoretical correlation matrix Sdep(ωs,ωi) by G(ωs,ωi) term by term, we can derive the modified theoretical correlation matrix Sdep(ωs,ωi) [see Fig. 3(b)]. The measured joint spectrum is shown in Fig. 3(c). In this measurement, the interval between two frequency components is changed to 5 pixels, which means that the resolution becomes 0.37 nm.

 figure: Fig. 3.

Fig. 3. Theoretical and experimental results of a filtered joint spectrum. (a) The theoretical spectrum reshaped by filters. The white curve is the spectrum transmission rate of the bandpass filter, centered at 779.5 nm and with a full width at half maximum (FWHM) of 3 nm. (b) and (c) are theoretical and experimental results of a joint spectral intensity matrix of correlated photons, respectively.

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The resolution of the correlation matrix is limited by both the grating and the pixels of the camera, which is 1024×1024. In practice, photon spots often take 2×2 or 3×3 pixels of the screen, and we choose this spot size to balance the acceptable frame rate and the resolution.

We can see that, as is shown in Figs. 2(d) and 3(c), the frequency components of signal and idler photons seem to be discrete rather than continuous. It is because we divide the continuous pattern into many segments, leading to the discontinuity of spectrum for both signal and idler photons. In order to restore it, a Fourier filter method is applied to the derived raw data. Since we have discarded all the useless information in the time space, leaving just the joint spectrum, our revised result is more smooth and clear (Fig. 4).

 figure: Fig. 4.

Fig. 4. Experimental results of correlation measurements with Fourier transformation. (a) and (b) show the corrected joint spectra of correlated photons without and with bandpass filters, respectively.

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The Schmidt number (SN) can be a good parameter to quantify our results. For the joint spectrum without adding bandpass filters, photons are highly entangled in the frequency domain. After calculating the eigenmodes and corresponding coefficients, the SN is derived. The theoretical SN is 3.519, and the SN of original data is 4.002±0.136. After a 2D Fourier filter, the SN of revised data is 3.370±0.110. After adding 3 nm bandpass filters, the entanglement in the frequency domain is released to some extent. Thus, the theoretical SN decreases to 1.419. But at the same time, these 3 nm bandpass filters also block many photons outside of the filter region. The original experimental data are not enough to derive meaningful decomposed eigenmodes because of large statistical fluctuations. Therefore, the Fourier transformation filter is applied to extract the profile of this joint spectrum. The SN of filtered data turns out to be 1.350±0.200, which is very well consistent with the theoretical value.

One interesting question to ask is if there is any possibility to further measure the complex phase pattern of the joint spectral amplitude. Although the current device deals with an intensity pattern, there have been works that use a spatial light modulator to encode and decode the phase-shaped wave front [38] and use a reference light to reconstruct the 2D phase structures [22]. Such reconstruction of a phase correlation pattern might be considered a second step of our methods.

4. DISCUSSION

In summary, we present an approach of mapping and measuring a large-scale photonic correlation with single-photon imaging. We demonstrate this by measuring the joint spectrum of correlated photons with direct imaging. Unlike previous works [3941], we do not have to move two detectors m and n times, respectively, to obtain a correlation matrix of m×n. Other than spectrum correlation, correlations on other spaces can also be detected after being mapped to position space. The ability to address large-scale correlations in two dimensions may boost the computational power of analog quantum computing by implementing the Boson sampling [24] and quantum walk [24] in very large spaces.

In addition to quantum technologies, COSPLI may find applications in exploring some new region of ultra-weak signals [42], like agriculture [43], food chemistry [44], and biomedicine [45]. For example, it has been reported that the neuronal activity has correlation with an ultra-weak photon emission (UPE). Commercial detectors have been able to observe the UPE from a cultured hippocampal slice. However, such research is limited within the detection of accumulation images [46] or a long-time-periods correlation without broader research scopes [47]. Instead, COSPLI may serve as an entirely new technique to reveal the phenomena where correlated events happen simultaneously.

Funding

National Key R&D Program of China (2017YFA0303700); National Natural Science Foundation of China (NSFC) (61734005, 11761141014, 11690033); Science and Technology Commission of Shanghai Municipality (STCSM) (15QA1402200, 16JC1400405, 17JC1400403); Shanghai Municipal Education Commission (16SG09, 2017-01-07-00-02-E00049); Zhiyuan Scholar Program (ZIRC2016-01); National Young 1000 Talents Plan.

Acknowledgment

The authors thank Brian Smith, Lijian Zhang, and Jian-Wei Pan for helpful discussions and suggestions.

 

See Supplement 1 for supporting content.

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44. T. Iida, Y. Yoshiki, S. Someya, and K. Okubo, “Generation of reactive oxygen species and photon emission from a browned product,” Biosci. Biotechnol. Biochem. 66, 1641–1645 (2002). [CrossRef]  

45. H. Ou-Yang, G. Stamatas, C. Saliou, and N. Kollias, “A chemiluminescence study of uva-induced oxidative stress in human skin in vivo,” J. Investig. Dermatol. 122, 1020–1029 (2004). [CrossRef]  

46. R. Tang and J. Dai, “Spatiotemporal imaging of glutamate-induced biophotonic activities and transmission in neural circuits,” PLoS ONE 9, 1–8 (2014). [CrossRef]  

47. A. Prasad and P. Pospišil, “Two-dimensional imaging of spontaneous ultra-weak photon emission from the human skin: role of reactive oxygen species,” J. Biophoton. 4, 840–849 (2011). [CrossRef]  

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    [Crossref]
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2018 (2)

H. Tang, X.-F. Lin, Z. Feng, J.-Y. Chen, J. Gao, K. Sun, C.-Y. Wang, P.-C. Lai, X.-Y. Xu, Y. Wang, L.-F. Qiao, A.-L. Yang, and X.-M. Jin, “Experimental two-dimensional quantum walk on a photonic chip,” Sci. Adv. 4, eaat3174 (2018).
[Crossref]

H.-S. Zhong, Y. Li, W. Li, L.-C. Peng, Z.-E. Su, Y. Hu, Y.-M. He, X. Ding, W. Zhang, H. Li, L. Zhang, Z. Wang, L. You, X.-L. Wang, X. Jiang, L. Li, Y.-A. Chen, N.-L. Liu, C.-Y. Lu, and J.-W. Pan, “12-photon entanglement and scalable scattershot boson sampling with optimal entangled-photon pairs from parametric down-conversion,” Phys. Rev. Lett. 121, 250505 (2018).
[Crossref]

2017 (3)

2016 (4)

J. Gao, L.-F. Qiao, X.-F. Lin, Z.-Q. Jiao, Z. Feng, Z. Zhou, Z.-W. Gao, X.-Y. Xu, Y. Chen, H. Tang, and X.-M. Jin, “Non-classical photon correlation in a two-dimensional photonic lattice,” Opt. Express 24, 12607–12616 (2016).
[Crossref]

E. Poem, T. Hiemstra, A. Eckstein, X.-M. Jin, and I. A. Walmsley, “Free-space spectro-temporal and spatio-temporal conversion for pulsed light,” Opt. Lett. 41, 4328–4331 (2016).
[Crossref]

R. Chrapkiewicz, M. Jachura, K. Banaszek, and W. Wasilewski, “Hologram of a single photon,” Nat. Photonics 10, 576–579 (2016).
[Crossref]

M. Jachura, R. Chrapkiewicz, R. Demkowicz-Dobrzański, W. Wasilewski, and K. Banaszek, “Mode engineering for realistic quantum-enhanced interferometry,” Nat. Commun. 7, 11411 (2016).
[Crossref]

2015 (4)

T. Gerrits, F. Marsili, V. B. Verma, L. K. Shalm, M. Shaw, R. P. Mirin, and S. W. Nam, “Spectral correlation measurements at the Hong-Ou-Mandel interference dip,” Phys. Rev. A 91, 013830 (2015).
[Crossref]

M. Jachura and R. Chrapkiewicz, “Shot-by-shot imaging of Hong-Ou–Mandel interference with an intensified sCMOS camera,” Opt. Lett. 40, 1540–1543 (2015).
[Crossref]

M. Bentivegna, N. Spagnolo, C. Vitelli, F. Flamini, N. Viggianiello, L. Latmiral, P. Mataloni, D. J. Brod, E. F. Galvão, A. Crespi, R. Ramponi, R. Osellame, and F. Sciarrino, “Experimental scattershot boson sampling,” Sci. Adv. 1, e1400255 (2015).
[Crossref]

M. Lebugle, M. Gräfe, R. Heilmann, A. Perez-Leija, S. Nolte, and A. Szameit, “Experimental observation of n00n state Bloch oscillations,” Nat. Commun. 6, 8273 (2015).
[Crossref]

2014 (5)

J. Carolan, J. D. A. Meinecke, P. J. Shadbolt, N. J. Russell, N. Ismail, K. Wörhoff, T. Rudolph, M. G. Thompson, J. L. O’Brien, J. C. F. Matthews, and A. Laing, “On the experimental verification of quantum complexity in linear optics,” Nat. Photonics 8, 621–626 (2014).
[Crossref]

K. Poulios, R. Keil, D. Fry, J. D. A. Meinecke, J. C. F. Matthews, A. Politi, M. Lobino, M. Gräfe, M. Heinrich, S. Nolte, A. Szameit, and J. L. O’Brien, “Quantum walks of correlated photon pairs in two-dimensional waveguide arrays,” Phys. Rev. Lett. 112, 143604 (2014).
[Crossref]

S. A. Goorden, M. Horstmann, A. P. Mosk, B. Škorić, and P. W. H. Pinkse, “Quantum-secure authentication of a physical unclonable key,” Optica 1, 421–424 (2014).
[Crossref]

M. Cifra and P. Pospíšil, “Ultra-weak photon emission from biological samples: Definition, mechanisms, properties, detection and applications,” J. Photochem. Photobiol. B 139, 2–10 (2014).
[Crossref]

R. Tang and J. Dai, “Spatiotemporal imaging of glutamate-induced biophotonic activities and transmission in neural circuits,” PLoS ONE 9, 1–8 (2014).
[Crossref]

2013 (5)

J. B. Spring, P. S. Salter, B. J. Metcalf, P. C. Humphreys, M. Moore, N. Thomas-Peter, M. Barbieri, X.-M. Jin, N. K. Langford, W. S. Kolthammer, M. J. Booth, and I. A. Walmsley, “On-chip low loss heralded source of pure single photons,” Opt. Express 21, 13522–13532 (2013).
[Crossref]

O. Schwartz, J. M. Levitt, R. Tenne, S. Itzhakov, Z. Deutsch, and D. Oron, “Superresolution microscopy with quantum emitters,” Nano Lett. 13, 5832–5836 (2013).
[Crossref]

M. A. Broome, A. Fedrizzi, S. Rahimi-Keshari, J. Dove, S. Aaronson, T. C. Ralph, and A. G. White, “Photonic boson sampling in a tunable circuit,” Science 339, 794–798 (2013).
[Crossref]

J. B. Spring, B. J. Metcalf, P. C. Humphreys, W. S. Kolthammer, X.-M. Jin, M. Barbieri, A. Datta, N. Thomas-Peter, N. K. Langford, D. Kundys, J. C. Gates, B. J. Smith, P. G. R. Smith, and I. A. Walmsley, “Boson sampling on a photonic chip,” Science 339, 798–801 (2013).
[Crossref]

N. Spagnolo, C. Vitelli, L. Sansoni, E. Maiorino, P. Mataloni, F. Sciarrino, D. J. Brod, E. F. Galvão, A. Crespi, R. Ramponi, and R. Osellame, “General rules for bosonic bunching in multimode interferometers,” Phys. Rev. Lett. 111, 130503 (2013).
[Crossref]

2012 (1)

M. P. Edgar, D. S. Tasca, F. Izdebski, R. E. Warburton, J. Leach, M. Agnew, G. S. Buller, R. W. Boyd, and M. J. Padgett, “Imaging high-dimensional spatial entanglement with a camera,” Nat. Commun. 3, 984 (2012).
[Crossref]

2011 (4)

A. Eckstein, A. Christ, P. J. Mosley, and C. Silberhorn, “Highly efficient single-pass source of pulsed single-mode twin beams of light,” Phys. Rev. Lett. 106, 013603 (2011).
[Crossref]

D. Stucki, M. Legré, F. Buntschu, B. Clausen, N. Felber, N. Gisin, L. Henzen, P. Junod, G. Litzistorf, P. Monbaron, L. Monat, J.-B. Page, D. Perroud, G. Ribordy, A. Rochas, S. Robyr, J. Tavares, R. Thew, P. Trinkler, S. Ventura, R. Voirol, N. Walenta, and H. Zbinden, “Long-term performance of the swiss quantum quantum key distribution network in a field environment,” New J. Phys. 13, 123001 (2011).
[Crossref]

J. O. Owens, M. A. Broome, D. N. Biggerstaff, M. E. Goggin, A. Fedrizzi, T. Linjordet, M. Ams, G. D. Marshall, J. Twamley, M. J. Withford, and A. G. White, “Two-photon quantum walks in an elliptical direct-write waveguide array,” New J. Phys. 13, 075003 (2011).
[Crossref]

A. Prasad and P. Pospišil, “Two-dimensional imaging of spontaneous ultra-weak photon emission from the human skin: role of reactive oxygen species,” J. Biophoton. 4, 840–849 (2011).
[Crossref]

2010 (5)

A. Peruzzo, M. Lobino, J. C. F. Matthews, N. Matsuda, A. Politi, K. Poulios, X.-Q. Zhou, Y. Lahini, N. Ismail, K. Wörhoff, Y. Bromberg, Y. Silberberg, M. G. Thompson, and J. L. OBrien, “Quantum walks of correlated photons,” Science 329, 1500–1503 (2010).
[Crossref]

M. Aßmann, F. Veit, M. Bayer, C. Gies, F. Jahnke, S. Reitzenstein, S. Höfling, L. Worschech, and A. Forchel, “Ultrafast tracking of second-order photon correlations in the emission of quantum-dot microresonator lasers,” Phys. Rev. B 81, 165314 (2010).
[Crossref]

X.-M. Jin, J.-G. Ren, B. Yang, Z.-H. Yi, F. Zhou, X.-F. Xu, S.-K. Wang, D. Yang, Y.-F. Hu, S. Jiang, T. Yang, H. Yin, K. Chen, C.-Z. Peng, and J.-W. Pan, “Experimental free-space quantum teleportation,” Nat. Photonics 4, 376–381 (2010).
[Crossref]

C. Wagenknecht, C.-M. Li, A. Reingruber, X.-H. Bao, A. Goebel, Y.-A. Chen, Q. Zhang, K. Chen, and J.-W. Pan, “Experimental demonstration of a heralded entanglement source,” Nat. Photonics 4, 549–552 (2010).
[Crossref]

S. Barz, G. Cronenberg, A. Zeilinger, and P. Walther, “Heralded generation of entangled photon pairs,” Nat. Photonics 4, 553–556 (2010).
[Crossref]

2009 (2)

M. Aßmann, F. Veit, M. Bayer, M. van der Poel, and J. M. Hvam, “Higher-order photon bunching in a semiconductor microcavity,” Science 325, 297–300 (2009).
[Crossref]

J. Wiersig, C. Gies, F. Jahnke, M. Aßmann, T. Berstermann, M. Bayer, C. Kistner, S. Reitzenstein, C. Schneider, S. Höfling, A. Forchel, C. Kruse, J. Kalden, and D. Hommel, “Direct observation of correlations between individual photon emission events of a microcavity laser,” Nature 460, 245–249 (2009).
[Crossref]

2008 (1)

P. J. Mosley, J. S. Lundeen, B. J. Smith, P. Wasylczyk, A. B. U’Ren, C. Silberhorn, and I. A. Walmsley, “Heralded generation of ultrafast single photons in pure quantum states,” Phys. Rev. Lett. 100, 133601 (2008).
[Crossref]

2006 (1)

2005 (2)

Y.-H. Kim and W. P. Grice, “Measurement of the spectral properties of the two-photon state generated via type ii spontaneous parametric downconversion,” Opt. Lett. 30, 908–910 (2005).
[Crossref]

C.-Z. Peng, T. Yang, X.-H. Bao, J. Zhang, X.-M. Jin, F.-Y. Feng, B. Yang, J. Yang, J. Yin, Q. Zhang, N. Li, B.-L. Tian, and J.-W. Pan, “Experimental free-space distribution of entangled photon pairs over 13  km: Towards satellite-based global quantum communication,” Phys. Rev. Lett. 94, 150501 (2005).
[Crossref]

2004 (1)

H. Ou-Yang, G. Stamatas, C. Saliou, and N. Kollias, “A chemiluminescence study of uva-induced oxidative stress in human skin in vivo,” J. Investig. Dermatol. 122, 1020–1029 (2004).
[Crossref]

2003 (1)

Y.-H. Kim, “Quantum interference with beamlike type-ii spontaneous parametric down-conversion,” Phys. Rev. A 68, 013804 (2003).
[Crossref]

2002 (2)

T. Ohya, S. Yoshida, R. Kawabata, H. Okabe, and S. Kai, “Biophoton emission due to drought injury in red beans: Possibility of early detection of drought injury,” Jpn. J. Appl. Phys. 41, 4766–4771 (2002).
[Crossref]

T. Iida, Y. Yoshiki, S. Someya, and K. Okubo, “Generation of reactive oxygen species and photon emission from a browned product,” Biosci. Biotechnol. Biochem. 66, 1641–1645 (2002).
[Crossref]

2001 (1)

W. P. Grice, A. B. U’Ren, and I. A. Walmsley, “Eliminating frequency and space-time correlations in multiphoton states,” Phys. Rev. A 64, 063815 (2001).
[Crossref]

1995 (1)

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 4337–4341 (1995).
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Supplementary Material (2)

NameDescription
» Supplement 1       Supplementary Materials
» Visualization 1       Kinetic one-shot imaging of joint spectrum with an ICCD

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Figures (4)

Fig. 1.
Fig. 1. (a) Schematic of COSPLI. (b)–(d) Sketched solutions of mapping different variables into positions. (b) Mapping frequency to position. (c) Mapping time to position. TDFS represents a time-dependent frequency shifter. (d) Mapping polarization to position. (e) Experimental setup of mapping frequency to position and joint spectrum measurement. A mode-lock Ti:sapphire oscillator centered at 780 nm, with a laser pulse duration of 130 fs and a repetition rate of 77 MHz, pumps a 1.3-mm-thick LiB 3 O 5 (LBO) crystal to double the laser frequency to 390 nm. The ultraviolet laser then pumps a 2-mm-thick β - BaB 2 O 4 (BBO) crystal to create identical photon pairs via a χ ( 2 ) Type 2 spontaneous parametric down-conversion process in the beam-like scheme [30]. The correlation of the frequency space of signal and idler photons is mapped into the correlation in the position space by a blazed grating with a line density of 1200 l/mm. (f) The spectra of signal and idler photons derived from the accumulated image. (g) (Top) An accumulated image with all spectral components. The upper and lower spots are signal and idler photons, respectively. (Middle) One of the frames that possess two registered photons. The two shiny spots are distributed in the two characterized areas in the accumulated image, respectively. (Bottom) The white grids define the resolution of the correlation measurement by dividing the mapped space into many individual parts.
Fig. 2.
Fig. 2. Theoretical and experimental results of the correlation measurement. (a) and (b) are theoretical and experimental results of a time-independent joint spectral intensity matrix of photons, respectively. The vertically elliptical shape suggests the photons share no correlation. (c) and (d) are theoretical and experimental results of a time-dependent joint spectral intensity matrix, respectively. The joint spectrum of correlated photons generated by BBO is an obliquely elliptical shape rather than a strict one-to-one relationship, because the two photons are not maximally correlated in the frequency space [34].
Fig. 3.
Fig. 3. Theoretical and experimental results of a filtered joint spectrum. (a) The theoretical spectrum reshaped by filters. The white curve is the spectrum transmission rate of the bandpass filter, centered at 779.5 nm and with a full width at half maximum (FWHM) of 3 nm. (b) and (c) are theoretical and experimental results of a joint spectral intensity matrix of correlated photons, respectively.
Fig. 4.
Fig. 4. Experimental results of correlation measurements with Fourier transformation. (a) and (b) show the corrected joint spectra of correlated photons without and with bandpass filters, respectively.

Equations (2)

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S dep ( ω s , ω i ) = | f ( ω s , ω i ) | 2 = | A α ( ω s + ω i ) ϕ ( ω s , ω i ) | 2 ,
S indep ( ω s , ω i ) = p s ( ω s ) p i ( ω i ) ,

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